A container has a volume of #18 L# and holds #6 mol# of gas. If the container is compressed such that its new volume is #3 L#, how many moles of gas must be released to maintain a constant temperature and pressure?

Question

A container has a volume of #18   L# and holds #6   mol# of gas.  If the container is compressed such that its new volume is #3 L#, how many moles of gas must be released to maintain a constant temperature and pressure?

Nathan Ashcroft · Accepted Answer

#5# moles

At constant temperature and pressure, we can use Avogadro's law, which states that #Vpropn# or #V_1/n_1=V_2/n_2# So, we need to find the new number of moles, and we can rearrange the equation into, #n_2=n_1/V_1*V_2# Now, we can substitute into the given values, and we get #n_2=(6 \ "mol")/(18color(red)cancelcolor(black)"L")*3color(red)cancelcolor(black)"L"# #=1 \ "mol"# So, the new amount of moles will be #1 \ "mol"#. In order to find the difference, #Deltan#, we use, #Deltan=n_2-n_1# #=1 \ "mol"-6 \ "mol"# #=-5 \ "mol"# So, five moles of the gas must be released.

Sebastian Acosta · Answer

undefined To maintain constant temperature and pressure, the number of moles of gas must remain constant. Therefore, the number of moles of gas released when the volume is compressed from 18 L to 3 L is 6 moles - (18 L / 3 L) = 6 moles - 6 moles = 0 moles. Thus, no moles of gas need to be released.